#63 정사각형 타일링

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#63 정사각형 타일링 | DOJ

DOJ/Beginner Contest DOJ/BCD 1

출제자: lunarlity

시간 제한: 2000 ms
메모리 제한: 1024 MB
체커: CUSTOM
정답 처리 점수: 100

Statement

KO EN

There is a rectangle of size $A \times B$ .

This rectangle will be filled with with square tiles without any remaining spaces. You can purchase square tiles as follows:

By paying a cost of $c$ , you receive $1$ square tile of size $c\times c$ .

Find the minimum cost required to fill the entire rectangle with square tiles without any remaining spaces.

Input

The input is given in the following format.

$A\ B$

Output

Print the minimum cost required.

Constraints

$1 \le A \le 10^{18}$ .
$1 \le B \le 10^{18}$ .

Subtasks

#	점수	제한
1	9	$A=B$ .
2	21	Either $A$ is a multiple of $B$ , or $B$ is a multiple of $A$ .
3	27	$A \leq 5 \ 000, \ B \leq 5 \ 000$ .
4	43	No additional constraints.

Samples

입력

6 4

출력

If you use $6$ square tiles with a side length of $2$ , the cost is $12$ . However, this is not optimal.

Instead, if you fill it with one square tile with a side length of $4$ and two square tiles with a side length of $2$ , the cost is $4+2+2=8$ . It can be shown that $8$ is the minimum cost.